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Title Particle Migration on Ice Surfaces

Author(s) ITAGAKI, Kazuhiko

Citation Physics of Snow and Ice : proceedings, 1(1), 233-246

Issue Date 1967

Doc URL http://hdl.handle.net/2115/20299

Type bulletin (article)

Note International Conference on Low Temperature Science. I. Conference on Physics of Snow and Ice, II. Conference onCryobiology. (August, 14-19, 1966, Sapporo, Japan)

File Information 1_p233-246.pdf

Hokkaido University Collection of Scholarly and Academic Papers : HUSCAP

Particle Migration on Ice Surfaces

Kazuhiko IT AGAKI

;jjX ~E jf!l ~

u.s. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., U.S.A.

Abstract

A novel phenomenon- is described which could indicate a new mechanism of mass flow along an ice surface. Glass beads evenly and randomly scattered on an ice surface migrate and tend to form pronounced clusters when the ice surface is exposed to an unsaturated atmosphere. Time lapse motion pictures reveal two types of migration of glass beads, smooth continuous and inter­mittent. Both types. of migration tend to form beads clusters. No movement is observed when the atmosphere is saturated with respect to ice.

Conventional mechanisms of surface mass flow such as evaporation-condensation and surface diffusion do -not appear to explain the migration. Volume diffusion in ice seems to be too slow a process, and liquid film flow is a rather improbable mechanism. Enhanced diffusivity of the surface layer is one possible mechanism.

I. Introduction

The surface of ice sometimes shows peculiar phenomena such as regelation. Re­

gelation _ has been discussed as evidence of a surface liquid layer by Faraday (1860),

Tyndall (18·58) or as proof of pressure -melting by Thomson (1859). Nakaya and Matsu­

moto, (1953) found that two ice spheres, suspended by strings and in contact, rotated

without separation when they were pulled apart. They attributed the phenomenon to

the existence of a liquid layer. From observations of the motion of a wire through ice

Telford and Turner (1963) were inclined to conclude that a fluid layer does exist on the

ice surface.

The following experiments could supply new knowledge about the ice surface. Pare

ticles on the subliming ice surface migrate along the surface and tend to coagulate into

clusters. Though the migration resembles the motion of particles suspended on a water

surface, several experimental results seem to indicate that mass flow in the relatively

thick high, diffusivity layer could be one possible mechanism. Some of the aforementioned

phenomena could be explained by the high diffusivity layer.

II. Experimental Procedure Sample preparation

The samples used in most of the experiments were ice single crystals produced in

the Mendenhall Glacier. The crystal is oriented by the reflection of light from frost

crystals grown on the ice surface (Nakaya, 1956), then cut by a band saw to the desired

orientation using a goniometric jig. The ice slabs thus cut are frozen onto 2 X 3 inch

glass slides applying -slight heat. The top surface of the ice sample is then microtomed.

234 K. ITAGAKI

When the basal or prismatic plane is desired, the Ice IS oriented to obtain a more ac­

curate plane by the frost, using a microscope with vertical illumination and adjustable

microtome stage. The accuracy is within 0.3 degree for the basal and prismatic planes

and about two degrees for the other orientations.

Glass beads, from 10 to 50011 in diameter, supplied by Cataphote Corporation,

Toledo, Ohio and Lapine and Company, Chicago, Illinois, are used. The glass beads

are generally perfect spheres; however, their surfaces are covered by particulate dirt.

Water used to wash the beads showed a high electrical conductivity, indicating that

some of the dirt is water soluble and electrolytic. The glass beads are spread evenly

and randomly on the ice surface immediately after the microtoming.

Two techniques are used to spread the glass beads. The method generally used is

to shake the beads onto a piece of urethane resin foam and keep them in the pores

until they are filliped off onto the ice surface. The second method is used when con­

tamination of the glass bead surface must be avoided or the beads are sticky because

of surface treatment. The desired amount of beads is put into a shallow vessel such

as the cap of a glass jar. A sharp fillipping blow on the bottom of the vessel about

10 cm aside from the ice surface spreads the beads evenly and randomly on the surface.

EXjJeriment 1: Untreated glass beads

The general features of glass bead migration can be seen in Figs. 1 a-d which are

obtained from a time lapse motion picture. The temperature was about -11°0 and the

humidity measured by a dew-point hygrometer shows frost point of about -16°C. A

a 0 hr b 10 hr

c 20 hr d 30 hr

Fig. 1. Migration of untreated glass beads. (x 55)

PARTICLE MIGRATION ON ICE SURFACES 235

slight motion of the air was indicated by the movement of tobacco smoke.

The migration can be classified as three types. The steady motion of individual

and clustered beads is observed generally, while there is a tendency for the single beads

and clusters to come together and form larger clusters. This type of movemet resembles

the movement of particles on a water surface supported by surface tension. The third

type is an intermittent motion. This can be expected if the supporting neck of the

bead is broken or bent by its own weight.

A side view of the migration of the beads is shown in Figs. 2 a-d. Three beads

designated A, Band C are seen close to the cross hair sticking to the left surface of

an ice block which appears as a dark field. Bead A, with a smaller bead sticking to it,

serves as a good reference mark for rotation. The thin neck supporting bead A can

be seen in Fig. 2 a. Beads A and B migrate toward the top of the photographs as the

ice surface recedes while C migrates toward the bottom of the picture until it disappears.

Although gravitational force is acting perpendicular to the photographs no preferential

migration occurs in the direction of the gravitational force because beads A and B

remain in focus.

Note that the smaller beads on A remain in the same position, which shows that

little rotation occurs. It IS observed from the time lapse motion picture that A moves

slowly but steadily while B moves rather intermittently.

Small specks appear on the ice surfaces after the microtome traces disappear; these

did not exist when the glass beads were spread. Some of the specks could be related

a 0 hr b 31 hr

c 35 hr d 44hr

Fig. 2. Side view of migration. (x 55)

236

a Omin

K. ITAGAKI

Fig. 3. Elongated speck.

b 40min

(x 170)

to the microtomed traces, which disappear during the sublimation of the surface. They

are rather uniform in size, but sometimes elongate to a short line as shown in Fig. 3 a.

Figure 3 b shows the same field as Fig. 3 a 40 minutes later. The short line tends to

resume its original shape.

Removal of a surface layer about 200-500 p, thick by sublimation is required to

produce these specks depending on the surface treatment and orientation. A very flat

surface usually appears after the traces of microtoming or lathing disappear. Etch

patterns which resemble the etch channels studied by Kuroiwa (1965) appear after 200-

500 p, of sublimation. These patterns spread in a relatively short time and become in­

dividual specks. The final density of the specks is about 105/cm2 which is the same order

of magnitude as the dislocation density obtained by Muguruma and Higashi (1961, 1963).

Two typical modes of movement of these specks are 1) rather straight with occa­

sional turning, and 2) circular motion around a fixed point. The number of specks does

not increase after the final density is attained, indicating that the foreign particles de­

posited on the ice surface cannot be the main cause of these specks. No clustering of

the specks is observed. These facts lead us to speculate that the specks are related to

dislocation. Assuming that the specks are dislocation etch pits, their movement shows

the time display of the sections of three-dimensional dislocation structures, because the

ice is receding by sublimation.

Experiment 2: Experiment in an ice-saturated atmosphere

The glass beads are spread on an ice surface by the same method as in experiment

1, then enclosed in a case with a glass window and surrounded by an ice wall to make

an ice-saturated atmosphere. Virtually no migration is observed, as shown in Figs. 4 a­

b, though dark fields appear around the glass beads. These dark fields originate from

surface modification due to mass transfer toward the supporting necks of the beads.

The large negative-curvature neck formed in the initial stage grows until the beads are

partially buried by ice, as shown in Fig. 5.

The material is supplied to the neck from the surrounding surfaces; thus the ice

surface is metamorphosed. The glass beads buried under the ice cover could not

move unless they were exposed to some driving force such as a temperature gradient

(Hoekstra, 1963).

PARTICLE MICRA TIO:--J O:--J ICE SURFACES 237

a 0 hr Ice saturated atmosphere b 50 hr

c 60 hr unsaturated atmosphere d 70hr

Fig. 4. Effect of humidity. (X55)

a Ohr b 2 hr

Fig. 5. Partially immersed beads in ice saturated atmosphere. (X170)

The migration of the glass beads starts only one hour after the removal of the ice

m case as shown in Figs. 4 c-d. The field is the same as Figs. 4 a-b. The dark field

around the beads reduces to a small shadow for the individual beads though it still

remains between the beads constituting clusters.

EXlJeriment 3: Effect of surface treatment

As mentioned earlier, considerable dirt is found on the surface of the glass beads

as received. Some of this is water soluble substances. There is a possibility that these

water soluble substances could dissolve into the ice surface and produce a liquid layer

because of melting point depression and that the glass beads are suspended on the

238 K ITAGAKI

liquid layer by surface tension. If this is the case the migration of the beads can be

attributed to the same mechanism that moves particles suspended on a water surface

by surface tension.

Glass beads are washed by bichromate-sulfuric acid and then by deionized water

until the electrical conductivity of wash water becomes 1 micromho. Then they are

dried in vacuum and spread on a microtomed ice surface. The migration of glass beads

thus treated appears the same as that of the untreated beads, indicating that the impurity

of the glass bead surface is not the major cause of glass bead migration. This is con­

firmed by other experiments. Larger glass beads are crushed above the microtomed ice

surface as shown in Fig. 6. Most of the shards thus produced are scattered on the ice

surface directly, thus there is little chance of contamination. As shown in Figs. 6 a-d,

the shards migrate as well as the glass beads though their shape is irregular.

a 0 hr b 8 hr

c 17 hr d 25 hr

Fig. 6. Migration of irregular shaped shards. (x 55)

After washing with deionized water, glass beads are coated with a very thin film of

silicone grease by immersing them in a dilute toluene solution of DC-7 and then vacu­

um dried. The DC-7-coated glass beads migrate and form clusters like the untreated

or bichromate-sulfuric acid treated beads; however, time lapse motion pictures reveal

that the migration is rather intermittent. This is in contrast to the clean-surfaced glass

beads such as those treated with bichromate-sulfuric acid or shards, which migrate con­

tinuously. The cause is not known.

Experiment 4: Jvligration of particles other than glass beads

To determine the effect of different materials on migration, experiments were

PARTICLE MIGRATION ON ICE SURFACES 239

o h1' a Teflon powder 15 hr

o hr b Formvar powder 15 hr

o hr c Silver iodide powder 2 hr

o hr d Mild steel filings 23 hr

Fig. 7. Migration of various kinds of particles. (x 55)

24.0 K. ITAGAKI

performed using Teflon powder, Formvar powder, silver iodide particles, filings of mild

steel, cotton filament and carbon black. All materials migrated though there might be

differences in migration velocity. The migration velocity is very difficult to define

because the movement is random and the temperature and humidity in the room are

not kept constant. Figures 7 a-d show migrating particles of various materials.

Experiment 5: l'vligration of glass beads sticking to a downward-facing ice surface

If migration is caused by the breaking or bending of the neck by the weight of the

bead, the beads would not migrate when the ice surface is facing downward. Figures

8 a-d show the migration in this case. Note that no beads are lost. Time lapse movies

show that movement is rather intermittent as with the DC-7-treated beads. The beads

are probably contaminated by a small amount of grease. Intermittent migration probably

caused by contamination of beads.

a 0 hr b lOhr

c 20 hr d 30 hr

Fig. 8. Migration on a downward facing surface. I X 55)

EXjJeriment 6': Effect of particle size on migration

Rate of migration seems to depend on the size of the bead. Smaller single beads

move actively while clusters and larger beads migrate slowly. As seen in Figs. 9 a-d,

the tendency of smaller beads to migrate toward larger ones could indicate mass flow

towards each bead by an unknown mechanism.

Experiment 7: lv1igration of other than spherical particles

Shards of larger glass beads crushed by a pair of pliers and spread on an ice surface

migrate as fast as beads of the same size stated in experiment 3. As shown in Figs.

PARTICLE MIGRATION ON ICE SURFACES

a 0 hr b 2 hr

c 4 hr d 6 hr

Fig. 9. Large and small beads

a 0 hr h 5 hr

c 10 hr

Fig. 10. Migration of glass fiber.

d 15 hr

(X55)

2L11

242 K. ITAGAKI

6 a-d long shards move somewhat sidewise. Short pieces of glass fiber also migrate

somewhat sidewise as shown in Figs. 10 a-d. As mention~d earlier, the larger beads

migrate more slowly. Lengthwise migration corresponds to migration of the larger

beads and thus will be slower, while sidewise migration corresponds to migration of

the smaller beads and thus will be faster.

Experiment 8: Migration under a temperature gradient

A temperature gradient was produced along the ice surface by sandwiching the ice

sample between metal plates, one of which has a small electric heater. Experiments

were made under temperature gradients of about 0.5 and 100°C/em. Ice surface were

exposed to an unsaturated atmosphere. The mean temperature between the plates is

about 2 and 4°C respectively higher than ambient temperature because of the heater.

The beads migrate definitely toward the colder plate. The mean migration rates for

beads of about 50 p. diameter are approximately 10-6 em/sec for a ,temperature gradient

of O.SoC/cm and 6 X 10 .. 6 em/sec for 100°C/em, though larger beads tend to migrate slower

than smaller beads.

III. Discussion

Eight possible mechanisms of particle migration were studied; some of these were

excluded by experiments or theoretical considerations while the others remain possible

explanations. The mechanisms are:

1. Rolling of glass beads on the ice surface following breaking or bending of their

supporting necks.

2. Drifting of glass beads on a liquid layer on the ice.

3. Migration of the beads supporting necks by evaporation-condensation.

4. Neck migration by surface diffusion.

5. Diffusion through bulk ice.

6. Mass flow in the glass/ice interface layer.

7. Neck migration due to bulk diffusion in the neck.

8. Migration of the beads by enhanced surface layer diffusion.

Mechanism 1. As was seen in experiment 5, no breaking of the neck is observed

when the ice surface is faced downward, yet the beads still migrate. If a bead made'

contact with the ice (other than at its neck) because of bending of the neck, it could be

considered a possible mechanism. This, however, would require rolling of the bead,

which was not observed in experiments 1 and 7. Thus the breaking or bending of

supporting necks is not responsible for migration of the beads.

Mechanism 2. According to Fletcher (1962) an ice surface is covered by a 100 A thick liquid film at O°C, and hydrophilic glass beads will be wetted by this film. The

force acting on a 40 p. diameter glass beads through the surface tension of this film is

of the order of 1 dyne, which will pull the bead to the solid ice surface. About 0.1

dyne of force would be required to move the bead without rolling, assuming the coefficient

of friction is 0.1. Applying Stokes' drag F=3-;rp.DU (F=force, p.=viscosity, D=diameter,

U = velocity), on this bead, and assuming it to be half immersed in the fluid, one obtains

U=3x102 cm/sec for p.=1.8x10- 2 dyne·sec/cm2, D=4X10-3 cm, F=10- 1 dyne. This ,is

PARTICLE MIGRATION ON ICE SURFACES 243

an extremely fast flow that would fill a 300 X 100 p. groove lying perpendicular to the

flow in one second! Hydrophobic glass beads could be supported on this layer by surface

tension and could drift with the flow. Observations, however, show that the speed of

migration is not this great but is of the same order of magnitude as that of the hydro­

philic beads, although the migration is intermittent. This mechanism is improbable.

Mechanism 3. The most operative mechanism of mass transfer on an ice surface

above -lOoe is evaporation-condensation (Itagaki, 1966). The neck supporting the bead

can be moved by evaporation from one side of it and condensation on the other side

caused by some driving force such as thermal gradient. However, this mechanism does

not move the neck as a unit but by transfer of individual molecules; thus it can cause

no movement of the bead without rolling.

Mechanism 4. Most of the sintering processes of metals are ascribed to surface

diffusion. However, the one-by-one process of surface diffusion, that is surface adsorbed

molecules migrating, cannot move the neck of a bead as a unit, and thus cannot cause

migration of the bead.

Mechanism 5. Several measurements have been made on marker movement in

metals under a strong thermal gradient (Brammer, 1960; Meechan and Lehman, 1962;

Shewmon, 1960; Swalin et al., 1965). One-dimensional atom current density per unit

time, J, (Meechan and Lehman, 1962, eq. (1),) is

D dT J= kT2). dy (LIE), (1)

where D is the self-diffusion coefficient, ). is the lattice spacing, T is the absolute tem­

perature, k is Boltzmann's constant, d T/dy is the temperature gradient, and LIE is the

algebraic sum of certain energies. This can be positive or negative for the vacancy

diffusion mechanism and negative for the interstitial mechanism. The maximum absolute

value ofLi E will be the activation energy of self-diffusion.

The presumable marker movement in ice due to this mechanism was calculated from

eq. (1) using ,D=10-11 cm2/sec, T=263°K, d T/dy=lce/cm, and LlE=15 kcal/mol. The

result is 1.1 X 10-12 cm/sec, which is of the order of 10-6 of the actual migration as

seen in experiment 8. This mechanism is too slow to explain bead migration.

Mechanism 6. As long as the bead remains on the ice surface while ice recedes by

sublimation, water'molecules must be removed from the supporting neck to maintain it

at a~ reasonable length. The molecules are probably removed from the interfacial layer

between bead and ice. Flow in the interfacial layer is necessary because the removal

of molecules must occur only from the edge of the interfacial layer, the surface of the

ice. If there is a predominant flow in one direction in the layer, the beads supported

by this layer may move with the flow. This layer could be 1) the liquid-like layer

discussed by previous researchers, 2) the crystallographic structure transformed gradually

to an amorphous structure in the layer, or 3) crystallographic periodicity in the layer. up

to the interface but with defect concentration greater than in the bulk of the ice.

Mechanis~ 7. The shape of the neck supporting the bead is symmetrical if no

disturbance' exists. However, nearby beads, etch pits, steps, etc. make the neck deviate

from its symmetrical shape, therefore, the total curvature of the neck becomes asymmetric.

244 K. ITAGAKI

The difference in curvature around the neck requires mass flow in and around the neck

toward the larger negative curvature because of the difference in surface free energy.

Although most of the mass flows through evaporation-condensation, the bulk of th~ ice

could contribute to the mass flow which would drift the neck as a whole and thus the

bead along the flow. As the diameter of the neck supporting a 40 p. bead is of· the

order of a few microns, the high diffusivity layer discussed m mechanism 8 could

enhance the bulk diffusivity in the neck.

Mechanism 8. Diffusivity in the crystal could be different near the surface and in

the bulk ice crystal. The surface could be the source or sink of point defects which

are responsible for diffusion. A different concentration of defects near the S!1rface would

change the diffusivity in this layer.

The vapor pressure of ice at O°C is 6.13 X 103 dyne/cm2 whi.cQ is produced by 2.3 X

1021 molecules/cm2·sec striking the surface. Assuming the surface barrier to be E b ,

r=N exp (-Eb/RT) will pass through the barrier and become interstitial where'r is the

production rate of excess interstitial molecules in the first layer, N is the number of

molecules striking the ice surface (2,3 X 1021/cm2·sec at O°C), R is the gas constant and T is the absolute temperature, The number of inteq;titial molecules that jump inward from

the first layer is [cl ny exp (- E j/RT)]/8 where C1 is the concentration of excess interstitial

molecules in the first layer, n is the number of molecules in the layer/cm2, y is the lattice

vibration frequency and E j is the energy required to jump into the' next layer. Layers

parallel to the '(0001) plane are assumed in this case, The number of molecules that

jump outward is [clny exp (-Eb/RT)]/8 and (6/8) [clcSny exp (-Es/RT)] will be absorbed

by the sink in the layer, where Cs is the concentration of sink and Eb and Es are the

energies required for the molecules to jump outward and into the sink respectively.

Assuming Eb=Ej=Es the exponential term can be written simply as {3 and the following

equation is obtained: / 1 1 N{3+ 8"" c2n~{3 = 8"" (cl ny{3+Cl ny{3+ 6cl csny(3), (2)

where C2 is the concentration of excess interstitials in the second layer. General terms

8N can be written by writing Co= ny as

(3)

Using, lattice spacing d, eq. (3) can be approximated as

d2 c Cs dx2 -6c(j2 = O. (4)

The solution is

(5)

17 1 10 15 From eq, (5) the effective thickness Xo= V&.= V 6 X 10-9 =4,1 X 10-4 cm assuming that

the concentration of the sink is 10-9 (~106/cm2), which is the concentration of disloca­

tions per lattice site in well annealed ice crystals (Muguruma, 1961; Muguruma and

Higashi, 1963). The average defect concentration in this layer is

PARTICLE MIGRATION ON ICE SURFACES

- cdx=- Co exp -- dx=co 1-- =-- 1--1 ),"0 1 ),"0 ( -x) (1) . 8N ( 1) Xo 0 Xo 0 Xo e n II e

I . h I b f b . 8 x 2.3 X 1021

(1 1) 116 10-5 nsertmg t e ~ame va ues as e ore we 0 tam 1015 X 1012 - (2.7) =. X .

245

(6)

This

is more than 104 times larger than the equilibrium values obtained from the self-diffusion

coefficient in bulk. Preliminary measurements of surface self-diffusion show it to be

about 105 times greater than the bulk diffusion constant. Mass flow in this thick high

diffusivity layer could move. the beads with the flow.

Mechanisms 6-8 remain possible. The present author, however, feels that mecha­

nism 6 is rather improbable. If a temperature gradient existed in the supporting inter­

face, the mass flow would be from the colder side t.o the warmer side because evapora­

tion from the warmer side would be faster. If there are no other local effects this flow

would move the beads toward the warmer side, which is contradictory to the observations

made in experiment 8.

Neither the materials of which the beads are made nor treatment of their surfaces

seem to have any effect on their migration, with the exception of silicone grease treat­

ment. This fact would also tend to exclude mechanism 6 because interfaces of different

materials would have different characteristics which would affect migration. The effect

of silicone grease could be attributed to uneven spreading of the grease on the ice sur­

face, which might have p!,oduced an 'uneven temperature distribution to drive the beads.

A thermal gradient drives particles from the warmer to the colder side. Migration

where there is no external thermal gradient could be attributed to local. temperature

differences due to an uneven surface around the beads. An uneven surface, i. e. one

with etch pits or steps, would cause uneven heat dissipation during sublimation, resultinlS

in an unequal temperature distribution. This random temperature distribution could

supply the driving force for random migration of the beads.

The author feels that the most probable mechanism in accord with the existing

experimental facts is mechanism 7 under the influence of enhanced surface layer diffusion

as discussed in, mechanism 8. However, a mechanism completely different from those

discussed here is still possible.

Acknowledgments

The author is indebted to Mr. J. M. Sayward for helpful discussions on the whole

man\lscript.

References

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5) HOEKSTRA, P. 1963 Movement of water in a film between glass and ice, Ph. D. Thesis,

246 K ITAGAKI

Cornell University.

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